Yi‐Cheng Zhang

Rui-Jie Wu, Gui-Yuan Shi, Yi-Cheng Zhang et al.

Numerical analysis of data from international trade and ecological networks has shown that the non-linear fitness-complexity metric is the best candidate to rank nodes by importance in bipartite networks that exhibit a nested structure. Despite its relevance for real networks, the mathematical properties of the metric and its variants remain largely unexplored. Here, we perform an analytic and numeric study of the fitness-complexity metric and a new variant, called minimal extremal metric. We rigorously derive exact expressions for node scores for perfectly nested networks and show that these expressions explain the non-trivial convergence properties of the metrics. A comparison between the fitness-complexity metric and the minimal extremal metric on real data reveals that the latter can produce improved rankings if the input data are reliable.

Rui Tang, Ziyun Yong, Shuyu Jiang et al.

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This problem, known as network alignment, holds significant importance. It enhances our understanding of complex system structures and behaviours, facilitates the validation and extension of theoretical physics research about studying complex systems, and fosters diverse practical applications across various fields. However, due to variations in the structure, characteristics, and properties of complex networks across different fields, the study of network alignment is often isolated within each domain, with even the terminologies and concepts lacking uniformity. This review comprehensively summarizes the latest advancements in network alignment research, focusing on analyzing network alignment characteristics and progress in various domains such as social network analysis, bioinformatics, computational linguistics and privacy protection. It provides a detailed analysis of various methods' implementation principles, processes, and performance differences, including structure consistency-based methods, network embedding-based methods, and graph neural network-based (GNN-based) methods. Additionally, the methods for network alignment under different conditions, such as in attributed networks, heterogeneous networks, directed networks, and dynamic networks, are presented. Furthermore, the challenges and the open issues for future studies are also discussed.

Manuel Sebastian Mariani, Matus Medo, Yi-Cheng Zhang

PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of science, the relation between the algorithm's efficacy and properties of the network on which it acts has not yet been fully understood. We study here PageRank's performance on a network model supported by real data, and show that realistic temporal effects make PageRank fail in individuating the most valuable nodes for a broad range of model parameters. Results on real data are in qualitative agreement with our model-based findings. This failure of PageRank reveals that the static approach to information filtering is inappropriate for a broad class of growing systems, and suggest that time-dependent algorithms that are based on the temporal linking patterns of these systems are needed to better rank the nodes.

Hao Liao, An Zeng, Yi-Cheng Zhang

Online reputation systems are commonly used by e-commerce providers nowadays. In order to generate an objective ranking of online items' quality according to users' ratings, many sophisticated algorithms have been proposed in the literature. In this paper, instead of proposing new algorithms we focus on a more fundamental problem: the rating projection. The basic idea is that even though the rating values given by users are linearly separated, the real preference of users to items between different values gave is nonlinear. We thus design an approach to project the original ratings of users to more representative values. This approach can be regarded as a data pretreatment method. Simulation in both artificial and real networks shows that the performance of the ranking algorithms can be improved when the projected ratings are used.

Hao Liao, An Zeng, Yi-Cheng Zhang

As a fundamental problem in many different fields, link prediction aims to estimate the likelihood of an existing link between two nodes based on the observed information. Since this problem is related to many applications ranging from uncovering missing data to predicting the evolution of networks, link prediction has been intensively investigated recently and many methods have been proposed so far. The essential challenge of link prediction is to estimate the similarity between nodes. Most of the existing methods are based on the common neighbor index and its variants. In this paper, we propose to calculate the similarity between nodes by the correlation coefficient. This method is found to be very effective when applied to calculate similarity based on high order paths. We finally fuse the correlation-based method with the resource allocation method, and find that the combined method can substantially outperform the existing methods, especially in sparse networks.

Wei Zeng, An Zeng, Ming-Sheng Shang et al.

During the past a few years, users' membership in the online system (i.e. the social groups that online users joined) are wildly investigated. Most of these works focus on the detection, formulation and growth of online communities. In this paper, we study users' membership in a coupled system which contains user-group and user-object bipartite networks. By linking users' membership information and their object selection, we find that the users who have collected only a few objects are more likely to be "influenced" by the membership when choosing objects. Moreover, we observe that some users may join many online communities though they collected few objects. Based on these findings, we design a social diffusion recommendation algorithm which can effectively solve the user cold-start problem. Finally, we propose a personalized combination of our method and the hybrid method in [PNAS 107, 4511 (2010)], which leads to a further improvement in the overall recommendation performance.